In a medium bowl, beat together the butter, sugar, egg, milk, and vanilla. Then add the flour (start with 2 cups), baking powder, and salt. Beat this until well blended. If the dough is still really sticky you may mix in another ¼ to ½ cup of flour.
In a large mixing bowl, sift together the powdered sugar and meringue powder. Add 5 tablespoons of warm water. Beat at high power for 10 minutes. When you are ready to ice/make the melted snow, drop a dollop of icing onto the middle of the cookie and carefully spread it out towards the edges. Place one marshmallow on each cookie to represent the head of the snowman.
Finished cookies can be stored for up to a week at room temperature when stored in an airtight container. You can also freeze them for up to 3 months.